(Abridged) Despite the privileged position that Lyman-alpha (Lya) emission line holds in the exploration of the distant universe and modern observational cosmology, the origin of the observed diversity of lya profiles remains to be thoroughly explained. Observations of nearby star forming galaxies bring their batch of apparent contradictions between Lya emission and their physical parameters, and call for a detailed understanding of the physical processes at work. IZw 18, one of the most metal-poor galaxies known is of particular interest in this context. We use a 3D Lya radiation transfer code to model Hubble Space Telescope (HST) observations of IZw 18 and to fit its Lya spectrum. Different geometrical configurations of the source and the neutral gas are explored. The integrated Lya profile of NW region of IZw 18 is reproduced using the observed small amount of dust (E(B-V) ~ 0.05) and a spherical HI shell with N(HI) = 6.5 x 10^(21) cm^(-2). Such a high column density makes it possible to transform a strong Lya emission (EW(Lya) = 60 A) into a damped absorption even with a small extinction. When a slab geometry is applied and a given line of sight is chosen, the Lya profile can be successfully reproduced with no dust at all and N(HI) = 3 x 10^(21) cm^(-2). The spatial variations of the profile shape are naturally explained by radiation transfer effects. In the case of outflowing Inter Stellar Medium (ISM), as commonly observed in Lyman Break Galaxies (LBGs), a high N(H) and dust content are required to observe Lya in absorption. For nearly static neutral gas as observed in IZw 18 and other low luminosity galaxies only a small amount of dust is required provided a sufficiently high N(H) covers the galaxy.
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